document.write( "Question 817740: If mary can drink a whole bottle of wine in 2 hours, and her friend jessica can drink a whole bottle of wine in 3 hours. How long will it take them to drink one bottle of wine together. \n" ); document.write( "
Algebra.Com's Answer #492168 by Theo(13342)\"\" \"About 
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mary can drink a whole bottle of wine in 2 hours.
\n" ); document.write( "jessica can drink a whole bottle of wine in 3 hours.
\n" ); document.write( "the rate that mary drinks a bottle of wine is equal to 1 bottle divided by 2 hours which is equal to 1/2. this means that mary drinks a half a bottle of wine per hour.
\n" ); document.write( "the rate that jessica drinks a bottle of wine is equal to 1 bottle divided by 3 hours which is equal to 1/3. this means that jessica drinks a third of a bottle of wine per hour.
\n" ); document.write( "obviously, mary drinks faster than jessica.
\n" ); document.write( "she can drink a half a bottle an hour while jessica can only drink a third of a bottle an hour.
\n" ); document.write( "when they drink together, their rates are additive.
\n" ); document.write( "this means that jessica and mary have a combined rate of 1/2 + 1/3 of a bottle per hour.
\n" ); document.write( "when you add 1/2 and 1/3 you need to get a common denominator so you multiply 1/2 by 3/3 and you multiply 1/3 by 2/2 and you get 3/6 + 2/6 which is equal to 5/6.
\n" ); document.write( "the combined rate of mary and jessica is therefore equal to 5/6 of a bottle per hour.
\n" ); document.write( "how long does it take them to drink a bottle together?
\n" ); document.write( "the formula is rate * time = units produced or consumed.
\n" ); document.write( "in this case, the rate is equal to 5/6 bottles per hour.
\n" ); document.write( "the time is what we want to find.
\n" ); document.write( "the units produced or consumed is equal to 1 bottle of wine.
\n" ); document.write( "the formula becomes
\n" ); document.write( "5/6 of a bottle consumed per hour * number of hours = 1 bottle of wine consumed.
\n" ); document.write( "algebraically, this is shown as:
\n" ); document.write( "5/6 * T = 1
\n" ); document.write( "this is derived from the formula R * T = Q, where R is equal to 5/6 and Q is equal to 1.
\n" ); document.write( "since only unknown, then you have to solve for T.
\n" ); document.write( "5/6 * T = 1 is the equation.
\n" ); document.write( "multiply both sides of this equation by 6/5 and you get:
\n" ); document.write( "6/5 * 5/6 * T = 6/5 * 1
\n" ); document.write( "simplify to get:
\n" ); document.write( "T = 6/5
\n" ); document.write( "it will take mary and jessica 6/5 of an hour to consume 1 bottle of wine when they drink from the same bottle together.
\n" ); document.write( "6/5 of an hours is equal to 1 hour and 1/5 of another hour which is equal to 1 hour and 1/5 * 60 minutes which is equal to one hour and 12 minutes.
\n" ); document.write( "let's look at the contribution of mary and jessica to the consumption of the bottle of wine.
\n" ); document.write( "we go back to the same equation of R * T = Q
\n" ); document.write( "mary consumes a bottle of wine at the rate of 1/2 bottle per hour.
\n" ); document.write( "the time is 6/5 of an hour.
\n" ); document.write( "her contribution is 1/2 * 6/5 = 3/5 of the bottle consumed in 6/5 of an hour.
\n" ); document.write( "jessica consumes a bottle of wine at the rate of 1/3 bottle per hour.
\n" ); document.write( "the time is 6/5 of an hour.
\n" ); document.write( "her contribution is 1/3 * 6/5 = 6/15 of the bottle which simplifies to 2/5 of the bottle.
\n" ); document.write( "in 6/5 of an hour, mary consumes 3/5 and jessica consumes 2/5 of the bottle.
\n" ); document.write( "add up their individual contributions to the consumption of the bottle and you see that the whole bottle has been consumed in 6/5 of an hour.\r
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